Author: Andrew Dados
Date: 09:52:03 02/04/01
Go up one level in this thread
On February 04, 2001 at 12:34:33, Andrew Dados wrote:
>On February 04, 2001 at 10:43:13, Ralf Elvsén wrote:
>
>>On February 03, 2001 at 04:35:45, Andrew Dados wrote:
>>>
>>>The base of ELO system is 'we need to assign some numbers to players that will
>>>obey Normal Distribution'. So you calculate ratings in that way.
>>
>>What are you saying here? That if we apply this rating system (based
>>on the formula below) the resulting numbers in the rating pool
>>will be normally distributed?
>>Or that we assume that the "true" ratings are normally distributed
>>and we therefore apply this system? Or something completely different?
>>
>>Ralf
>
>I'm saying here that rating numbers are not 'given' just like e.g. sizes of
>leaves. When building rating system we have to define it. So it is defined in
>the way that rating numbers agree with normal distribution; we also define
>standard deviation (which scales our system) and average rating. So your second
>sentence is correct.
If we were talking about players weight, then we start with some set of
numbers. We can calculate some statistical perperties of that set: average,
sigma, etc. Here process is totally reversed. We start with some game scores and
try to assign numbers which will be in agreement with normal distribution.
>
>-Andrew-
>
>>
>>>
>>>You can take it as definition of ELO system. If you need some numbers which obey
>>>different distribution, then you can devise your own rating system, but ELO
>>>definitely obeys normal distribution of ratings (as it defines ratings in that
>>>way).
>>>
>>>Practically for fide and uscf standard deviation (sigma) is about 280. That's
>>>what simplified formula of 1/(1+10^(-k/400.0)) used to calculate ratings
>>>implies.
>>>
>>>If you ever used Mathematica this is the 'real thing':
>>>(sig is Sigma)
>>>
>>>Dist[X_]=1/(sig*(2*Pi)^0.5)*Exp[-X*X/(2*sig*sig)];
>>>P[D_]=Integrate[Dist[X],{X,0,D}]+0.5; (* Integration from 0 to D *)
>>>
>>>You definitely have your point about 'not enough data to anchor sigma' thing,
>>>but for starters and for most real life match scores you can even simplify that
>>>'normal distribution' model and say: all rating differences are distributed
>>>equally. Within the range of +-200 ELO difference and around most programs
>>>strength (being way above avg of 1740 rating) it will be valid enough to draw
>>>conclusions....
>>>
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.